Nuprl Lemma : comb_for_int_op_wf
λg,a,e,z. a x(*;e;~) e ∈ g:Group{i} ⟶ a:ℤ ⟶ e:|g| ⟶ (↓True) ⟶ |g|
Proof
Definitions occuring in Statement :
int_op: i x(op;id;inv) e,
grp: Group{i},
grp_inv: ~,
grp_id: e,
grp_op: *,
grp_car: |g|,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
grp: Group{i},
mon: Mon
Lemmas referenced :
int_op_wf,
squash_wf,
true_wf,
grp_car_wf,
grp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
setElimination,
rename,
intEquality
Latex:
\mlambda{}g,a,e,z. a x(*;e;\msim{}) e \mmember{} g:Group\{i\} {}\mrightarrow{} a:\mBbbZ{} {}\mrightarrow{} e:|g| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |g|
Date html generated:
2016_05_15-PM-00_15_35
Last ObjectModification:
2015_12_26-PM-11_40_13
Theory : groups_1
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