Nuprl Lemma : comb_for_mk_perm_wf
λT,f,b,z. mk_perm(f;b) ∈ T:Type ⟶ f:(T ⟶ T) ⟶ b:(T ⟶ T) ⟶ (↓True) ⟶ perm_sig(T)
Proof
Definitions occuring in Statement :
mk_perm: mk_perm(f;b),
perm_sig: perm_sig(T),
squash: ↓T,
true: True,
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],
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
mk_perm_wf,
squash_wf,
true_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
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{}True) {}\mrightarrow{} perm\_sig(T)
Date html generated:
2019_10_16-PM-00_58_41
Last ObjectModification:
2018_10_08-AM-09_46_36
Theory : perms_1
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