Nuprl Lemma : polyform-subtype
∀[n,m:ℕ]. polyform(n) ⊆r polyform(m) supposing n ≤ m
Proof
Definitions occuring in Statement :
polyform: polyform(n),
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
polyform: polyform(n),
all: ∀x:A. B[x],
implies: P ⇒ Q,
nat: ℕ,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
and: P ∧ Q,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
cand: A c∧ B,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A
Lemmas referenced :
assert_wf,
ispolyform_wf,
polyform_wf,
le_wf,
nat_wf,
tree-induction,
all_wf,
tree_wf,
ispolyform_leaf_lemma,
tree_leaf_wf,
ispolyform_node_lemma,
iff_transitivity,
band_wf,
subtract_wf,
lt_int_wf,
less_than_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_lt_int,
tree_node_wf,
nat_properties,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
decidable__le,
itermSubtract_wf,
int_term_value_subtract_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
independent_functionElimination,
extract_by_obid,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
functionEquality,
lambdaFormation,
voidElimination,
voidEquality,
natural_numberEquality,
productEquality,
independent_pairFormation,
productElimination,
independent_isectElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
computeAll
Latex:
\mforall{}[n,m:\mBbbN{}]. polyform(n) \msubseteq{}r polyform(m) supposing n \mleq{} m
Date html generated:
2017_10_01-AM-08_32_19
Last ObjectModification:
2017_05_02-PM-03_18_35
Theory : integer!polynomial!trees
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