Nuprl Lemma : comb_for_compose_wf
λA,B,C,f,g,z. (f o g) ∈ A:Type ⟶ B:Type ⟶ C:Type ⟶ f:(B ⟶ C) ⟶ g:(A ⟶ B) ⟶ (↓True) ⟶ A ⟶ C
Proof
Definitions occuring in Statement :
compose: f o g,
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,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
compose_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
Error :functionIsType,
Error :inhabitedIsType,
universeEquality
Latex:
\mlambda{}A,B,C,f,g,z. (f o g) \mmember{} A:Type {}\mrightarrow{} B:Type {}\mrightarrow{} C:Type {}\mrightarrow{} f:(B {}\mrightarrow{} C) {}\mrightarrow{} g:(A {}\mrightarrow{} B) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} A {}\mrightarrow{} C
Date html generated:
2019_06_20-PM-00_26_16
Last ObjectModification:
2018_09_28-PM-11_40_36
Theory : fun_1
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