Nuprl Lemma : mklist-general_add1
∀[n:ℕ+]. ∀[f:Top]. (mklist-general(n;f) ~ mklist-general(n - 1;f) @ [f mklist-general(n - 1;f)])
Proof
Definitions occuring in Statement :
mklist-general: mklist-general(n;h),
append: as @ bs,
cons: [a / b],
nil: [],
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
nat: ℕ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
nat_plus_wf,
top_wf,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_plus_properties,
subtract_wf,
mklist-general-add1,
subtract-add-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
hypothesis,
dependent_set_memberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[f:Top]. (mklist-general(n;f) \msim{} mklist-general(n - 1;f) @ [f mklist-general(n - 1;f)])
Date html generated:
2016_05_14-PM-01_44_11
Last ObjectModification:
2016_01_15-AM-08_21_44
Theory : list_1
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