Nuprl Lemma : prank_functionality
∀[P,Q:formula()]. prank(P) ≤ prank(Q) supposing P ⊆ Q
Proof
Definitions occuring in Statement :
psub: a ⊆ b,
prank: prank(x),
formula: formula(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
and: P ∧ Q,
nat: ℕ,
less_than: a < b,
squash: ↓T,
le: A ≤ B
Lemmas referenced :
prank-psub,
decidable__le,
prank_wf,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
and_wf,
equal_wf,
formula_wf,
nat_wf,
le_wf,
intformand_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
less_than'_wf,
psub_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
unionElimination,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
setElimination,
rename,
productElimination,
setEquality,
equalityTransitivity,
hyp_replacement,
Error :applyLambdaEquality,
imageElimination,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[P,Q:formula()]. prank(P) \mleq{} prank(Q) supposing P \msubseteq{} Q
Date html generated:
2016_10_25-AM-11_21_55
Last ObjectModification:
2016_07_12-AM-07_28_05
Theory : general
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