Nuprl Lemma : comb_for_mk_perm_wf_a
λT,f,b,z. mk_perm(f;b) ∈ T:Type ⟶ f:(T ⟶ T) ⟶ b:(T ⟶ T) ⟶ (↓InvFuns(T;T;f;b)) ⟶ Perm(T)
Proof
Definitions occuring in Statement :
mk_perm: mk_perm(f;b),
perm: Perm(T),
inv_funs: InvFuns(A;B;f;g),
squash: ↓T,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
mk_perm_wf_a,
squash_wf,
inv_funs_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isectElimination,
inhabitedIsType,
functionIsType,
universeEquality
Latex:
\mlambda{}T,f,b,z. mk\_perm(f;b) \mmember{} T:Type {}\mrightarrow{} f:(T {}\mrightarrow{} T) {}\mrightarrow{} b:(T {}\mrightarrow{} T) {}\mrightarrow{} (\mdownarrow{}InvFuns(T;T;f;b)) {}\mrightarrow{} Perm(T)
Date html generated:
2019_10_16-PM-00_58_44
Last ObjectModification:
2018_10_08-AM-09_46_34
Theory : perms_1
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