Nuprl Lemma : qadd_inv_assoc_q
∀[a,b:ℚ]. (((a + -(a) + b) = b ∈ ℚ) ∧ ((-(a) + a + b) = b ∈ ℚ))
Proof
Definitions occuring in Statement :
qmul: r * s,
qadd: r + s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
minus: -n,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
abgrp: AbGrp,
iabgrp: IAbGrp{i},
grp: Group{i},
igrp: IGroup,
mon: Mon,
imon: IMonoid,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
grp_inv: ~,
infix_ap: x f y
Lemmas referenced :
iabgrp_op_inv_assoc,
qadd_grp_wf,
subtype_rel_self,
iabgrp_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
applyEquality,
sqequalRule,
instantiate
Latex:
\mforall{}[a,b:\mBbbQ{}]. (((a + -(a) + b) = b) \mwedge{} ((-(a) + a + b) = b))
Date html generated:
2020_05_20-AM-09_14_06
Last ObjectModification:
2020_02_04-PM-02_00_13
Theory : rationals
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